The comparison of interdependent correlations between optimal linear composites

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.This research was supported in part by an operating grant (#67-4640) to the first author from the National Sciences and Engineering Research Council of Canada. The authors would also like to acknowledge the helpful comments and encouragement of Alexander Shapiro, Stanley Nash, and Ingram Olkin.     

Asymptotic null distribution of person fit statistics with estimated person parameter

Person fit statistics are considered for dichotomous item response models. The asymptotic null distribution is derived for statistics which are linear in the item responses, and in which the ability parameter is replaced by an estimate. This allows the asymptotically correct standardization of linear person fit statistics with estimated ability parameter. The fact that the ability parameter is estimated usually decreases the asymptotic variance.I am indebted to Herbert Hoijtink and three anonymous referees for their comments on a previous version.     

Hamlet: plea for a measure of normality

The author first considers issues in psychoanalytic interpretations of literary characters, especially the question of treating the character as fiction (the aesthetic illusion) or as a real person. The position he adopts is to interpret Hamlet as a potential person, created by Shakespeare and an expression of Shakespeare’s actual – and intuitive – view of man.

With a synopsis of the tragedy and the context of its creation as background, the author then reflects on questions concerning the play. How does Shakespeare present the characters? Is Hamlet’s madness pretended or real? Which conflicts does he handle in the course of the play? Has Oedipal dynamics a role as motivational factor in his mind?

Hamlet is irrational, impulsive, emotional, inhibited, brooding, suspicious, revengeful, condemning and much more. But, in the view of the author, he is all this in a human, ‘normal’ way. There is nothing convincingly pathological or constricted in his character. ‘Un-normal’ is his intelligence and his wit. Hamlet – an intelligent, reflected, resourceful prince in late Renaissance – who has wrestle with a madhouse of political intrigues, family murders and deceitful friends.

Hamlet in Shakespeare’s text – a fairly normal person in quite a mad world.     

Leadership perceptions,gender, and dominant personality: The role of normality evaluations

Individuals with dominant personality tend to be perceived as leaders, but theory suggests the dominance advantage for leadership might depend upon gender. Role congruity theory (Eagly & Karau, 2002) holds that gender role-incongruence (i.e., dominant personality traits among women) can be a liability, which we propose produces a dominance-gender interaction effect on leadership perceptions. We extend this theory by proposing and testing a novel conceptual mediator of the role congruity effect—perceived normality. Results show dominance predicts perceived transformational leadership, but only for men. This role congruity interaction effect is then explained by perceived normality (mediated moderation). The conditional indirect effect of dominance on leadership through perceived normality is positive for men, but negative for women—consistent with role congruity theory.     

Standard errors of fit indices using residuals in structural equation modeling

The asymptotic standard errors of the correlation residuals and Bentler's standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals. Using these results, approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method. Further, in mean structures, approximations of the asymptotic standard errors of residuals, standardized residuals and their summary statistics are derived in a similar manner. Simulations are carried out, which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance, correlation and mean structures are close to actual ones.The author is indebted to the reviewers for their comments and suggestions which have led to an improvement of this work.     

Testing the assumptions underlying tetrachoric correlations

A method is proposed for empirically testing the appropriateness of using tetrachoric correlations for a set of dichotomous variables. Trivariate marginal information is used to get a set of one-degree of freedom chi-square tests of the underlying normality. It is argued that such tests should preferrably preceed further modeling of tetrachorics, for example, modeling by factor analysis. The assumptions are tested in some real and simulated data.Presented at the Psychometric Society meeting in Santa Barbara, California, June 25–26, 1984. The research of the first author was supported by Grant No. SES-8312583 from the National Science Foundation.     

A comparison of generalized and modified sample biserial correlation estimators

In a recent paper, Bedrick derived the asymptotic distribution of Lord's modified sample biserial correlation estimator and studied its efficiency for bivariate normal populations. We present a more detailed examination of the properties of Lord's estimator and several competitors, including Brogden's estimator. We show that Lord's estimator is more efficient for three nonnormal distributions than a generalization of Pearson's sample biserial estimator. In addition, Lord's estimator is reasonably efficient relative to the maximum likelihood estimator for these distributions. These conclusions are consistent with Bedrick's results for the bivariate normal distribution. We also study the small sample bias and variance of Lord's estimator, and the coverage properties of several confidence interval estimates.The author would like to thank the referees for several suggestions that improved the paper.     

Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions

During the last fifteen years, Akaike's entropy-based Information Criterion (AIC) has had a fundamental impact in statistical model evaluation problems. This paper studies the general theory of the AIC procedure and provides its analytical extensions in two ways without violating Akaike's main principles. These extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the “true” models. These selection criteria are called CAIC and CAICF. Asymptotic properties of AIC and its extensions are investigated, and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different Monte Carlo experiments under different conditions.     

Technology in Medicine: Ontology,Epistemology, Ethics and Social Philosophy at the Crossroads

In reference to the different approaches in philosophy(of medicine) of the nature of (medical) technology,this article introduces the topic of this specialissue of Theoretical Medicine and Bioethics, that is,the way the different forms of medical technologyfunction in everyday medical practice. The authorselaborate on the active role technology plays inshaping our views on disease, illness, and the body,whence in shaping our world.